While you are certainly able to edit the template in its default location, i would suggest as a 'best practice' that you assign it to an external template in the same location as any other external templates you are using. You never know if you might forget that you changed it, and when you upgrade as Georgi mentioned, your template will be overwritten.
even if you aren't prone to forgetting someone else may someday upgrade it and not realize changes were made.
you can set the control template in the properties of the control by clicking edit. Alternativelly, as I did on our sites, you can embed the control directly on the master page:
|<%@ Register tagprefix="cc" namespace="Telerik.Search.WebControls" assembly="Telerik.Search" %>
|<cc:SearchBox ID="SearchBox1" runat="server" IndexCatalogue="MySearch"
ResultUrl="~/Search.aspx" LayoutTemplatePath="~/Templates/Public/Search/SearchBox.ascx" />
this way all your templates are always in one separate place, and don't get overwritten.
hope this was helpful!